Best Known (22, 22+4, s)-Nets in Base 8
(22, 22+4, 8388602)-Net over F8 — Constructive and digital
Digital (22, 26, 8388602)-net over F8, using
- net defined by OOA [i] based on linear OOA(826, 8388602, F8, 4, 4) (dual of [(8388602, 4), 33554382, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(826, 8388602, F8, 3, 4) (dual of [(8388602, 3), 25165780, 5]-NRT-code), using
- trace code [i] based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- trace code [i] based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(826, 8388602, F8, 3, 4) (dual of [(8388602, 3), 25165780, 5]-NRT-code), using
(22, 22+4, large)-Net over F8 — Digital
Digital (22, 26, large)-net over F8, using
- 81 times duplication [i] based on digital (21, 25, large)-net over F8, using
- net defined by OOA [i] based on linear OOA(825, large, F8, 4, 4), using
- appending kth column [i] based on linear OOA(825, large, F8, 3, 4), using
- net defined by OOA [i] based on linear OOA(825, large, F8, 4, 4), using
(22, 22+4, large)-Net in Base 8 — Upper bound on s
There is no (22, 26, large)-net in base 8, because
- 2 times m-reduction [i] would yield (22, 24, large)-net in base 8, but